I've watched all the episodes on Crunchy Roll (SAO and ALO) and I think I missed something.
The character Yui acts as though she is the child of Asuna and Kirito. I do not remember Yui in the SAO arc, but perhaps I missed it.
When did Asuna and Kirito have a child? How did that child get special access to the system?
Yui is certainly a part of the SAO arc - she appears in it quite prominently.
She is found by Kirito and Asuna and they "adopt" her in SAO, though she turns out to not be exactly what she appears to be.
She is, in fact a program. A mental health assistance program (who has been disallowed from doing its job when SAO was locked down). This explains her special system access and knowledge.
Because of her programming, she is somehow sentimental which makes it possible for her to want to be part of a family and stay with Asuna and Kirito.
Well, the question is already answered but I will try to explain more details...
Both the game and the NerveGear were created by Akihiko Kayaba.
so we can say the cardinal system and Yui were also created by Akihiko Kayaba.
Yui was programmed to understand and learn human emotions and mental health but later Yui was locked to just to read and do not have any access to the system to help people log out in case it is affecting their health. while reading everyone mental health she found that there are two human Kirito and Asuna who were happy and enjoying their life in this virtual world and everyone else is scared of death and just want to go out of this shitty game. some of them even lose hope and committed suicide. So Yui wants to be part of the Asuna and Kirito. she met them purposely to go close to them. When they found her they thought she is just some lost child, they tried to find her parents but later during a battle in dungeon Yui saved Asuna and kirito ( she was an immortal object in the game and defeated very high-level monster with ease ) Cardinal was AI software to and is able to recognize that Yui programmed is having some bug so they decided to delete her. But kirito plays and smart move and saved her all data in his SAO profile. Because of Yui Kirito able to understand the reality of Akihiko Kayaba who was playing a leader role in no.1 clan in the game just to make people fool ( he was immortal object too that is why kirito loss duel against him) later when kirito won sword art he found out 300 people still not awakened by the game including Asuna. later he found out the image of Asuna inside another RPG game. He started to play that game in search Asuna and he found out that the game is having all of his previous data and skills of sword art online except items. so he tried to find out Yui data in his profile. after finding her data he activated Yui back. who read all the information about this game and told him that this game is having copy data of SAO and turned herself into pixie so that the game not able to find about her. Yui also told Kirito that her data is now saved inside local memory of Kirito nervegear.
